Abstract: Tame pairs of groups were introduced to study the missing boundary problem for covers of compact 3-manifolds. In this paper we prove that if is an exact sequence of infinite finitely presented groups or if is an ascending HNN-extension with base and is a certain type of finitely presented subgroup of , then the pair is tame.

Also we develop a technique for showing certain groups cannot be the fundamental group of a compact 3-manifold. In particular, we give an elementary proof of the result of R. Bieri, W. Neumann and R. Strebel:

A strictly ascending HNN-extension cannot be the fundamental group of a compact 3-manifold.